section 3.2
=0.81, which is below
the hard-disk fluid-solid transition at 
=0.87 [56],
to 
=0.95, well above the melting density.
The other simulation parameters were the same as in the two
dimensional square-well solid simulation.To simulate the fluid in three dimensions, we used a system of 108 square-well spheres in a periodic cubic box. The density was varied from
=0.9 to 
=1.0 and the well
width ranged from 
=0.01 to 
=0.06. The simulation
parameters were equal to those chosen for the solid simulations.
For both the 2D and 3D simulations the initial random configuration
was compressed to the required density and equilibrated for 20,000
cycles before data was collected in a production run of 20,000 cycles.
To calculate the fluid-solid coexistence one needs the absolute free
energy of both the reference fluid and the reference solid phase. For
the free energy of the hard disk fluid we used a Padé
approximation proposed by Hoover and Ree [56].
The hard disk solid free energy was obtained from simulation data by
Alder et al. [55].
The free energy of the hard-sphere fluid was calculated using the
accurate Carnahan-Starling equation of state [37], whereas
the Hall equation of state [54] was used in the solid region
together with an absolute free energy value obtained from simulations
of Frenkel and Ladd [39].Using these reference free energies and the simulated average internal energies in eqn. 3.2 we were able to obtain the coexistence curves for the fluid-solid transition for both the two and three dimensional square-well models.
phase diagrams for
triangular lattice of 200 square well particles in two dimensions.
Starting with the coexistence curve on the right, from right to left
the curves correspond to the well widths 
=0.01, 0.02,
0.03, 0.04, 0.05, 0.06 and 0.07. Solid-fluid coexistence curves are
shown for all systems with 
0.03. The critical
points are indicated by filled circles, the triple points by open circles.
phase diagrams for the
fcc structure of 108 square well particles. Starting with the
coexistence curve on the right, from right to left the curves
correspond to the well widths 
=0.01, 0.02, 0.03, 0.04,
0.05 and 0.06. The upper dashed fluid-solid coexistence curve refers
to a well width of 
=0.07 and shows that the
solid-solid transition has become metastable at this point. The
critical points are indicated by filled circles, the triple points by
open circles. The critical point at 
, corresponding to 
=0 was computed using the lattice
model described in section